The moving-baseline localization (MBL) problem arises when a group of
nodes moves through an environment in which no external coordinate
reference is available. When group members cannot see or hear one
another directly, each node must employ local sensing and inter-device
communication to infer the spatial relationship and motion of all
other nodes with respect to itself.

We consider a setting in which nodes move with piecewise-linear
velocities in the plane, and any node can exchange noisy range estimates
with certain sufficiently nearby nodes. We develop a distributed solution to the
MBL problem in the plane, in which each node performs robust hyperbola
fitting, trilateration with velocity constraints, and subgraph alignment
to arrive at a globally consistent view of the network expressed in its
own “rest frame.” Changes in any node's motion cause deviations
between observed and predicted ranges at nearby nodes, triggering
revision of the trajectory estimates computed by all nodes.

We implement and analyze our algorithm in a simulation informed by the
characteristics of a commercially available ultra-wideband (UWB) radio,
and show that recovering node trajectories, rather than just locations,
requires substantially less computation at each node. Finally, we
quantify the minimum ranging rate and local network density required for
the method's successful operation.